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\begin{equation*}\mathbf{F} = \frac{d}{dt}(m\mathbf{v}) 
 = m\frac{d\mathbf{v}}{dt} + \mathbf{v}\frac{dm}{dt} 
 = m\mathbf{a} + \mathbf{v}\frac{dm}{dt} \end{equation*}
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